[tex]\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}[/tex]
$A=\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}
\\\Rightarrow A^2=16+2\sqrt{(8+2\sqrt{10+2\sqrt{5}})(8-2\sqrt{10+2\sqrt{5}})}
\\=16+2\sqrt{24-8\sqrt{5}}=16+2\sqrt{(2\sqrt{5}-2)^2}
\\=12+4\sqrt 5=(\sqrt{10}+\sqrt 2)^2
\\\Rightarrow A=\sqrt{10}+\sqrt 2$